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homework2summer2006 - Economics 302 4 Week Summer Session...

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Economics 302 4 Week Summer Session 2006 Homework #2 Due Monday, June 5, 2006 5/31/06 Homework will be graded for content as well as neatness. Sloppy or illegible work will not receive full credit. This homework requires the use of Excel which is a spreadsheet program. 1. (2 points) Suppose that the production function for an economy is given by Y = F(K, N, A) = AK 1/2 N 1/2 where Y is output, K is capital, N is labor, and A is the level of technology. a. Suppose that the value of A is equal to 1. Fill in the table below based on this information and the given production function. Labor Capital Output MPN Using a Derivative MPN using the change in output/change in labor 0 25 ---- ---- 4 25 9 25 16 25 25 25 36 25 b. Suppose that the value of A increases to 10. Fill in the table below based on this information and the given production function. Labor Capital Output MPN Using a Derivative MPN using the change in output/change in labor 0 25 ---- ---- 4 25 9 25 16 25 25 25 36 25 c. Draw a picture of the two production function relationships you computed in parts (a) and (b) placing output on the vertical axis and labor on the horizontal axis. Verbally explain the effects of a change in technology on the aggregate production function. d. In the tables you computed the MPN using a derivative and the MPN using a formula for discrete data (the change in output/the change in labor). Provide an explanation for why these two measures would not be equivalent and use a graphical explanation to explore what would make these two measures numerically closer to one another. 1
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2. (5 points) Suppose that the production function for an economy is given by Y = F(K, N, A) = K 1/2 N 1/2 A where Y is output, K is capital, N is labor, and A is the level of technology.
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